If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x.

Question:

If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using this value of x, find the mode of the data.

Solution:

We know that,

Mean $=\frac{\text { Sum of observations }}{\text { Number of observations }}$

The given data is 3, 21, 25, 17, (x + 3), 19, (x – 4).

Mean of the given data $=\frac{3+21+25+17+(x+3)+19+(x-4)}{7}$

$\Rightarrow 18(7)=84+2 x$

$\Rightarrow 126-84=2 x$

$\Rightarrow 2 x=42$

$\Rightarrow x=21$

Hence, the value of x is 21.

Now, the given data is 3, 21, 25, 17, 24, 19, 17
Arranging this data in ascending order:
3, 17, 17, 19, 21, 24, 25

Here, 17 occurs maximum number of times.
∴ Mode = 17

Hence, the mode of the data is 17.

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